[FOM] Richard Epstein's view

Sara L. Uckelman S.L.Uckelman at uvt.nl
Thu Apr 5 08:30:08 EDT 2012

On 04/02/2012 04:40 PM, Timothy Y. Chow wrote:
>> Buridan discusses the insoluble "Every proposition is affirmative,
>> therefore no proposition is negative."  Such an inference is problematic
>> on Buridan's view because of the token-based approach to propositions
>> that he (and other medieval logicians) took.  It is certainly *possible*
>> that every (token) proposition that happens to exist is affirmative, and
>> thus it is *possible* that no proposition is negative, but it will never
>> be possibly-true that no proposition is negative, for in order for this
>> proposition to have a truth value, it must exist, and it itself is
>> negative, and thus its very existence falsifies itself.
> I don't find this objection convincing.

Indeed, Buridan's justification (that God could destroy all tokens of
negative propositions) is not one that is readily acceptable today; this
is why I framed a similar example in terms of assertions.  While it is
surely unlikely that all assertions (at the time of evaluation of an
assertion) are affirmative, I would think that the burden of proof
would be on the person who claims that such an unlikely scenario is
impossible, not on the one who claims it's possible.

 > In particular, I would blame the
> implicit theory of "possibility" being invoked here, rather than the
> theory of truth.  In what sense is it possible that every proposition that
> happens to exist is affirmative?

In my paper that I cited in the other email [1], models are given in
terms of sheets of paper that have (token) propositions inscribed on
them; there is nothing inconsistent with a sheet of paper that has only
affirmative statements written on it.  It is, as you note below, a
variant of the idea of possible worlds, which is a relatively orthodox
way of making semantic sense of possibility.

 > Presumably, some version of the theory
> of possible worlds, currently very fashionable in philosophy, is being
> appealed to.  But I don't see why we should think that such a theory is
> relevant to a discussion of mathematical statements.  For example, all

I took the point of your earlier message as to be giving a theory of
truth which would be able to encompass a particular view about the truth
of mathematical statements, in which case being able to deal with
possibility is a necessary component.  If not via possible world, than
via some other means, but I would not be surprised if similar puzzles
couldn't be cooked up for those other means.


[1] http://www.springerlink.com/content/138522713223v015/

Dr. Sara L. Uckelman
Tilburg Center for Logic and Philosophy of Science
Tilburg University

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